It of course could be both.
If you just sat down in the game and you don't know the player you are kind of in the dark with this one and need to have a very narrow range of hands that you are going to call with. Like playing online, you calculate your risk.
However after you have played with the player for awhile you will be able to be more accurate with what is going on. Most if any players do not freeze every hand on the river. So just the fact that they have turned into a statue may give you a clue to the strength of their hand. What kind of statue they are may also give you a clue. They may turn into a statue that is staring at you, or a statue that is staring someplace else.
Having said that, if there is any tell to be had here it is in the persons eyes. Generally speaking if the person can't sincerely look you in the eye they are bluffing. Emphasis on sincerity in their eyes. It is a well known tell that a player who cannot look you in the eyes is bluffing that the more sophisticated players know, and they will look you in the eye. But the eyes are wonderful things that project mood and emotion in very subtle ways. So you often can get a good accurate tell when the look you in the eyes on a bluff.
Most good players are rather consistent with the stance they have after they have made a bet, rather it is the bet the OP described or not. However if they tend to turn into a statue looking away, and other times facing you in the action, it can be telling. If they are looking away it will often mean that they have the nuts or are on a stone bluff, its not critical to them what happens, you are either going to call or not and watching that is not important. If they face the action, they may be concerned about the strength of the hand, it is strong but not the nuts and they want to be in a position to better determine what to do if you raise.
It is important to say that the tells for most of us poor mortals in the situation described are terribly unreliable. It is important to repeat that the more you know about the player the more accurate your conclusions will be in this situation. Most of the information you need is collected before the player turns into a statue, while they are still moving, stacking chips to push, fidgeting, or whatever it is they tend to do or not do right before they make the push.